I'm equally mystified about that distinction.
The "of" does seem to be common/uncommon/preferred/rejected/accepted in a number of phrases depending on which side of the Atlantic you're on.
Get off of the bus -- becoming increasingly common and accepted here. The BrE speakers can't seem to avoid commenting on the horror of it.
A couple of times -- seems preferred here, but rejected there
Half the time -- no of, referring to how many seconds, acceptable/preferred here
One-tenth the time -- no of, referring to how many seconds (days, etc.), accepted here.
Half of the time -- with of, referring to 50% of the occurrences, seems required everywhere?
Could this PLEASE not become one of the threads where people snipe back and forth about whose version is correct?